Thermoelectric Inks and Power Factor Tunability in Hybrid Films through All Solution Process

Thermoelectric (TE) materials can have a strong benefit to harvest thermal energy if they can be applied to large areas without losing their performance over time. One way of achieving large-area films is through hybrid materials, where a blend of TE materials with polymers can be applied as coating. Here, we present the development of all solution-processed TE ink and hybrid films with varying contents of TE Sb2Te3 and Bi2Te3 nanomaterials, along with their characterization. Using (1-methoxy-2-propyl) acetate (MPA) as the solvent and poly (methyl methacrylate) as the durable polymer, large-area homogeneous hybrid TE films have been fabricated. The conductivity and TE power factor improve with nanoparticle volume fraction, peaking around 60–70% solid material fill factor. For larger fill factors, the conductivity drops, possibly because of an increase in the interface resistance through interface defects and reduced connectivity between the platelets in the medium. The use of dodecanethiol (DDT) as an additive in the ink formulation enabled an improvement in the electrical conductivity through modification of interfaces and the compactness of the resultant films, leading to a 4–5 times increase in the power factor for both p- and n-type hybrid TE films, respectively. The observed trends were captured by combining percolation theory with analytical resistive theory, with the above assumption of increasing interface resistance and connectivity with polymer volume reduction. The results obtained on these hybrid films open a new low-cost route to produce and implement TE coatings on a large scale, which can be ideal for driving flexible, large-area energy scavenging technologies such as personal medical devices and the IoT.

S-3 dev. of 0.7 µm), and Bi2Te3 exhibited average particle size about 200 nm (with std. dev. of 95 nm). In both the cases the thickness of the platelets is around 50-70 nm. Crystallite size was estimated from the XRD data, using Williamson-Hall plot, in the range 160-600 nm, with a weighted average of about 200 nm for Sb2Te3 , while it is in the range of 50-100 nm with a weighted average of 70 nm for Bi2Te3. Due to the anisotropy in the particle morphology the crystallites are also expected to exhibit some anisotropy, the obtained size being viable in the lateral plane.

Percolation Theory
As the system shows significant value of a percolation threshold, we are inclined to consider that direction/model. The critical exponent in a percolation system is assumed to depend only on the dimensionality of the lattice and is independent of the details of the lattice structure. 1 Namely, for 3D systems the critical exponent acquires values between 1.6 and 2.0 and, for 2D systems, the critical exponent varies between 1.1 and 1.3. 2 However, in conducting systems the critical exponent does not follow the universal trend. 3 In systems based on insulating matrices with embedded conductive fillers and where the conduction process is controlled by interfiller tunneling, the inverted Swiss-cheese model can be applied, which predicts values of the critical exponent between 0.8 and 1. 2 An example is found in a work published by Wang et al. 4 in which S-5 carbon nanotubes were introduced into a transparent PVDF matrix. In his case, the critical exponent has a value of 0.85, similar to that obtained by us when we use Bi2Te3 nanoparticles.
The system can be considered 2D since the ratio between the thickness and the width of the film is very small. After the new measurements of electrical conductivity using the 4-point technique, the percolation curve settings have been updated in Figure 4 and the values of the critical exponent are close to 1.
When the percolation threshold of Sb2Te3 and Bi2Te3 hybrid films with the DDT linker are compared, the values obtained for Sb2Te3 are lower than that of Bi2Te3. As the percolation threshold depends on the particle size, the results suggest that Bi2Te3 nanoparticles are smaller than Sb2Te3. This was confirmed by the SEM micrographs of as-made Sb2Te3 and Bi2Te3 nanoparticles presented in Figure S3. In order to demonstrate the viability of this suggested outcome, we chose Sb2Te3 -PMMA system for control experiments. We synthesized smaller Sb2Te3 platelets, by using the same synthetic process and only lowering the concentration of the precursors to half. DLS measurements are performed on the suspensions of previous and new batch of Sb2Te3 nanoparticles in isopropanol. Results are presented in Figure S4a, where the peak average dispersed size (by approximation to the volume of a sphere) of smaller sample is about 200 nm lower than the large ones used for the percolation study. Thereafter, a hybrid film is developed by using this and adapting the best performing film composition with 60% Sb2Te3 in the PMMA matrix, without the addition of DDT. The hybrid film with larger platelets showed a resistance of 600 W, while the films with smaller platelets showed about 600 kW ( Figure   S4b), which is about three orders of magnitude higher. This finding confirms the predictions S-6 by the percolation theory, which allows the design of platelets of various lateral size to systematically study this correlation as a further research work. Figure S5. Flexibility test as a function of a) bending cycles and b) bending radius.

Flexibility Tests
As a proof of concept, two flexibility tests have been carried out on Sb2Te3 -PMMA hybrid film with 60% Sb2Te3 content and DDT linker. For this, the deposition of the ink has been applied to a flexible PET substrate. Figure S5a shows the results of (2.5 cm long hybrid film on PET substrate) bending the film 3000 times on a 2 cm diameter cylinder and measuring the change in electrical conductivity after every 100 bendings. The conductivity of the film gradually decreases with the number of flexes until reaching a loss in electrical conductivity of 50% after 3000 flexes. On the other hand, Figure S5b shows the variation of electrical conductivity as a function of the bending radius. In this case, the electrical conductivity also decreases as the bending radius decreases and a loss of electrical conductivity by 70% is reached when the bending radius is as small as 1 cm. These results clearly indicate that formulated hybrid films based on Sb2Te3 (and Bi2Te3) nanoparticles with DDT and in the PMMA matrix are not particularly flexible. However, we must remember that a film composed solely of Sb2Te3 (or Bi2Te3) nanoparticles deposited on a flexible substrate such as PET would almost completely lose electrical conductivity after a few bending cycles, since in this case there would be no glue effect of the polymeric matrix. In addition, we must remember that the polymeric matrix, PMMA, used in this work is a matrix that is rigid at room temperature since its glass transition temperature, Tg, is around 110 ºC. 5 Therefore, the developed hybrid-films will only have a S-7 flexible behavior when the working temperature is higher than 110 ºC since it is at this temperature when the polymeric matrix begins to be more fluid and, therefore, can be handled without breaking. With the choice of other flexible polymers as the matrix a higher flexibility could be achieved, with much less degradation of the transport performance.

Transport Property Evaluation
The electronic transport properties of the hybrid films were determined by the measurement of electrical conductivity ( ) and the Seebeck coefficient (S). The was determined by the Van der Pauw equation (Eq. S1), inserting four equidistant contacts of conductive silver paint on the surface of the films ( Figure S6). Next, a current was applied between two points and the potential between the other two points was measured, obtaining R1. To obtain R2, we applied a current intensity between two other points and the potential between the remaining two was measured. Knowing the values of R1, R2 and the thickness (d), the electrical resistivity ( ) of the film was obtained, which was then converted to electrical conductivity.
(b) Voltage as a function of the current to determine R1 and R2.
The S was determined at room temperature using a homemade system consisting of two copper blocks (Figure S7). One of the copper blocks was heated by a Peltier module while the other was kept at room temperature. The temperature values at the hot and cold end of the S-8 samples were recorded using two K-type thermocouples connected to PicoLog software. The hot-side temperature was gradually increased to reach a gradient of 60 °C by applying a voltage to the Peltier module with a source supplier (Keithley 2280S). The S potential generated was recorded with a Keithley 2450 source meter. By plotting the S voltage generated as a function of the temperature gradient, a linear distribution was obtained, where slope is the S. Figure S7. (a) Scheme of the home-made set up to measure the Seebeck coefficient.
(b) Voltage generated as a function of the temperature difference, where the sloop is the Seebeck coefficient.
In order to optimize the thermoelectric films, the influence of the film thickness on the electrical conductivity was studied by varying the number of layers deposited on the substrate. Figure   S8 represents the study carried out previously to the percolation curve for the hybrid films containing 60wt% Sb2Te3 or Bi2Te3 nanoparticles. It was observed that for both the Sb2Te3